I have one there ay vgyh but didn't know they rented lockers unless you had a boat in the yard or slip. But I never asked, so would be worth a try. Ours is 60$ per month.
There used to be a company on tortola that would bring a large trunk like container to your boat on arrival and then pick it up with your contents when finished with charter. Not sure of the name.
Try Store It BVI 284-443-4684. Or jollymon@surfbvi.com They are also on Facebook I have not used them but received a quote a year ago. It was $350 a year for storage and $25 delivery fee, For a plastic container 48" x 22" x 22". They also have larger storage spaces available.
I'll have to check my records for the namelater, but I used storage based close to Moorings next to Compton Marine for two seasons and it was reasonably cheap.